Theta - Fuzzy Associative Memory: Fundamentals, Extensions, and Applications

• Grant number: 14/10067-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2014
• End date: January 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Peter Sussner
• Grantee: Estevão Esmi Laureano
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Associative memories (AMs) are mathematical models geared to storing desired input-outputpairs called fundamental memories. In addition, some error correction capability is also desiredfor an AM model. In this project we will investigate in detail a class of AMs called $\Theta$-fuzzy associative memories ($\Theta$-FAMs), that correspond to mappings between classes of fuzzy sets given by two-layer fuzzy neural networks. Under some conditions, a -FAM has optimal absolute storage capability and is able to achieve perfect recall for noisy input patterns that are sufficiently close to uncorrupted pattern cues. The $\Theta$-FAMs models were successfully applied in many classification problems including several benchmarks and some real world applications such as vision-based robot self-localization, classification of time series of vegetaion indixes and speaker recognition. In this project we will extend -FAMs models in two ways: topologically and conceptually. The first extension aims at providing further degrees of freedom and flexibility of architecture forregression problems. The second extension refers to the use of the $\Theta$-FAM approach as the $\Theta$-FAM mathematical model of inference for general classes of information granules based on lattice theory.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SUSSNER, PETER; ESMI, ESTEVAO; BARROS, LAECIO C.; IEEE. Controlling the Width of the Sum of Interactive Fuzzy Numbers with Applications to Fuzzy Initial Value Problems. 2016 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), v. N/A, p. 8-pg., 2016-01-01. (14/10067-8)

ESMI, ESTEVAO; SUSSNER, PETER; DIAS IGNACIO, GUSTAVO BARROSO; DE BARROS, LAECIO CARVALHO. A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems. FUZZY SETS AND SYSTEMS, v. 331, p. 85-104, JAN 15 2018. (14/10067-8)